Find column with maximum sum in a Matrix

Given a N*N matrix. The task is to find the index of column with maximum sum. That is the column whose sum of elements are maximum.

Examples:

Input : mat[][] = {
        { 1, 2, 3, 4, 5 },
        { 5, 3, 1, 4, 2 },
        { 5, 6, 7, 8, 9 },
        { 0, 6, 3, 4, 12 },
        { 9, 7, 12, 4, 3 },
    };
Output : Column 5 has max sum 31

Input : mat[][] = {
        { 1, 2, 3 },
        { 4, 2, 1 },
        { 5, 6, 7 },
    };
Output : Column 3 has max sum 11

The idea is to traverse the matrix column-wise and find the sum of elements in each column and check for every column if current sum is greater than the maximum sum obtained till the current column and update the maximum_sum accordingly.

Below is the implementation of the above approach:

C++

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// C++ program to find column with
// max sum in a matrix
#include <bits/stdc++.h>
using namespace std;
  
#define N 5 // No of rows and column
  
// Function to find the column with max sum
pair<int, int> colMaxSum(int mat[N][N])
{
    // Variable to store index of column
    // with maximum
    int idx = -1;
  
    // Variable to store max sum
    int maxSum = INT_MIN;
  
    // Traverse matrix column wise
    for (int i = 0; i < N; i++) {
        int sum = 0;
  
        // calculate sum of column
        for (int j = 0; j < N; j++) {
            sum += mat[j][i];
        }
  
        // Update maxSum if it is less than
        // current sum
        if (sum > maxSum) {
            maxSum = sum;
  
            // store index
            idx = i;
        }
    }
  
    pair<int, int> res;
  
    res = make_pair(idx, maxSum);
  
    // return result
    return res;
}
  
// driver code
int main()
{
  
    int mat[N][N] = {
        { 1, 2, 3, 4, 5 },
        { 5, 3, 1, 4, 2 },
        { 5, 6, 7, 8, 9 },
        { 0, 6, 3, 4, 12 },
        { 9, 7, 12, 4, 3 },
    };
  
    pair<int, int> ans = colMaxSum(mat);
  
    cout << "Column " << ans.first + 1 << " has max sum "
         << ans.second;
  
    return 0;
}

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Java

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// Java program to find column 
// with max sum in a matrix 
import java.util.*;
  
class GFG
{
// No of rows and column 
static final int N = 5
  
// structure for pair
static class Pair
{
    int first , second;
      
    Pair(int f, int s)
    {
        first = f;
        second = s;
    }
}
  
// Function to find the column
// with max sum 
static Pair colMaxSum(int mat[][]) 
    // Variable to store index of
    // column with maximum 
    int idx = -1
  
    // Variable to store max sum 
    int maxSum = Integer.MIN_VALUE; 
  
    // Traverse matrix column wise 
    for (int i = 0; i < N; i++)
    
        int sum = 0
  
        // calculate sum of column 
        for (int j = 0; j < N; j++)
        
            sum += mat[j][i]; 
        
  
        // Update maxSum if it is 
        // less than current sum 
        if (sum > maxSum) 
        
            maxSum = sum; 
  
            // store index 
            idx = i; 
        
    
  
    Pair res; 
  
    res = new Pair(idx, maxSum); 
  
    // return result 
    return res; 
  
// Driver code 
public static void main(String args[])
    int mat[][] = { { 1, 2, 3, 4, 5 }, 
                    { 5, 3, 1, 4, 2 }, 
                    { 5, 6, 7, 8, 9 }, 
                    { 0, 6, 3, 4, 12 }, 
                    { 9, 7, 12, 4, 3 }}; 
  
    Pair ans = colMaxSum(mat); 
  
    System.out.println("Column " + (int)(ans.first + 1) +
                           " has max sum " + ans.second); 
}
  
// This code is contributed
// by Arnab Kundu

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Python3

# Python3 program to find column with
# max Sum in a matrix

N = 5

# Function to find the column with max Sum
def colMaxSum(mat):

# Variable to store index of column
# with maximum
idx = -1

# Variable to store max Sum
maxSum = -10**9

# Traverse matrix column wise
for i in range(N):

Sum = 0

# calculate Sum of column
for j in range(N):
Sum += mat[j][i]

# Update maxSum if it is less
# than current Sum
if (Sum > maxSum):
maxSum = Sum

# store index
idx = i

# return result
return idx, maxSum

# Driver Code

mat = [[ 1, 2, 3, 4, 5 ],
[ 5, 3, 1, 4, 2 ],
[ 5, 6, 7, 8, 9 ],
[ 0, 6, 3, 4, 12 ],
[ 9, 7, 12, 4, 3 ]]

ans, ans0 = colMaxSum(mat)

print(“Column”, ans + 1,
“has max Sum”, ans0)

# This code is contributed by
# Mohit kumar 29

Output:

Column 5 has max sum 31


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